Wave Motion
Elements of a Wave Amplitude The maximum displacement of a particle from mean position is called as Amplitude of a transverse Wave . The maximum pressure exerted on medium is called as Amplitude of a longitudinal Wave . Period The time taken for the execution of one complete wave is called as Time Period . Frequency The number of waves executed per second is called as Frequency of he wave . Wavelength The distance traversed by one complete wave is called as wavelength . Wave Number The number of waves passing through 1 metre of medium is called as wave number . It is the reciprocal of wavelength (in metres) Velocity The velocity of a wave is the displacement of the ave per unit time . Phase Periodicity Path Difference and Phase Difference Phase Difference = ( 2π / λ ) Path Difference Where (2π / λ ) is the propagation constant Types of waves Longitudinal Velocity = v = sqrt T/μ where μ is the linear charge density Transverse Simple Harmonic Progressive Waves A Simple Harmonic Motion is periodic in space as well as in time . This property is called double periodicity . Displacement : y = a sin2π - x/λ Reflection of Waves For transverse waves , the wave is reflected back in the same phase . For longitudinal Waves , the wave is reflected back in the same phase ; but if at the other end of boundary , there exists a rarer medium , the reverse condition will be valid . Superposition of Waves When two or more waves travelling through a medium arrive at a point of the medium simultaneously , each wave produces its own displacement , independently of others . Hence , the resultant displacement at that point is equal to the vector sum of the displacements due to all the waves . Beats The alternate waxing and waning of sound after definite intervals of time , due to superposition of two waves of nearly equal frequencies , is called production of beats . The number of times the sound waxes or wanes in one second is called as frequency of waves . y = R sin 2π nt ; where n is the average frequency of superposing waves , t is the time period of beat . N = n1 - n2 Imax α (a1+a2)2 Imin α (a1-a2)2 Doppler Effect na = ± vo / v ∓ vs If the source and observer are approaching each other , numerator has addition . If the source and observer are moving apart from each other , numerator has subtraction . Stationary Waves When 2 identical progressive waves both travelling in opposite directions , interfere with each other , by superposition of waves resultant wave obtained in the form of loops is called a Stationary Wave . Strings Laws of Vibrating Strings Air Column Vibrations Resonance If the resonance frequencies of a body are in the ratio xa : xb : xc , then x is the frequency of the body . Tips and Tricks Category:Physics